Radiology, Private Equity, and the Prisoner’s Dilemma

Last week, Dr. Ashutosh Rao from Quantum Radiology wrote an email with an interesting take on the corporate ownership of radiology practices as seen through the lens of Game Theory. He was gracious enough to allow me to share a version of it here for your enjoyment.


For decades, the unwritten covenant between private practice partners (owners) and new hires (associates) was that a practice that had been built and maintained for years by owners would be handed off to associates to build and maintain for yet another generation of partners. This prior stable equilibrium [Cooperate, Cooperate] has been disrupted (by yield-hungry investors) and we have a new stable equilibrium [Defect, Defect].

The available equilibria:

  • Stable equilibrium #1 [Cooperate, Cooperate]: Practice owners build for the future. Associates build for the future.
  • Unstable equilibrium #1 [Cooperate, Defect]: Practice owners build for the future. Associates won’t build for the future; they are clock-in/clock-out.
  • Unstable equilibrium #2 [Defect, Cooperate]: Practice owners don’t care about the future and sell the practice for $$$. Associates who wanted to build for the future are shut out.
  • Stable equilibrium #2 [Defect, Defect]: Practice owners extract what they can from the practice. Associates extract what they can from the practice.

Accusation: Owners (often pejoratively grouped as “boomers”) have screwed their associates by allowing working conditions to deteriorate and then selling out.

Accusation: Associates (often dismissed as “millennials”) just want to clock in and clock out and don’t care about the practice, so owners should sell before the practice deteriorates.

And so here we are. From “The Prisoner’s Dilemma”:

Defection always results in a better payoff than cooperation, so it is a strictly dominant strategy for both players. Mutual defection is the only strong Nash equilibrium in the game. Since the collectively ideal result of mutual cooperation is irrational from a self-interested standpoint, this Nash equilibrium is not Pareto efficient.


Thanks again to Dr. Rao.

In game theory, a Nash equilibrium is the outcome in which no player can benefit from unilaterally changing their choice. Pareto efficiency refers to a situation in which it’s not possible to make any individual better off without making someone else worse off.

The Prisoner’s dilemma is an example of a game that is not Pareto efficient: the optimal outcome for the field of radiology would be for both parties to cooperate. If only. Unfortunately, a series of individually rational choices doesn’t always lead to the best collective outcome.



Guy Borders 08.24.23 Reply

I think perhaps the premise of this article accepts the assumption that theft is moral.

Hiring Radiologists (no buyout) already onsite running their own practice and offering them 50% less in a market where Radiologists are need more than ever is bound to create market disruptions…Healthcare or othewise.

I say this as a lot of Private practices are not given buyouts and are independently owned and whether it is the government or a Government sponsored entity (Private equity) saying, ‘we’re here from the government and we are here to help you’ translates into ‘we know what you are making from your professional fee and we want a large slice of it for nothing because we now own your contract through our back room MBA buddy deals’.

That happened to our group.
Did we ask for it, no.
Did we want it, no.
Did we quit and look for something else, yes.
Did it hurt the local community healthcare, yes. (I use the metric asking the question, ‘whether doctors would send family and friend into the hospitals now run with outsourced behometh Private equity groups?’)

Are we adapting, yes. We are seeking to work as a seasoned group of Radiologists together with other independently owned Radiology groups holding contracts not given away yet. A 15% haircut is better than 50% in our opinion. We act as ‘capacitors’ to alleviate workloads on groups holding the contracts.

Don’t believe the MBA marketers showing only the lens they want. In the end it is legalized theft from a Radiologists standpoint.

Guy Borders MD
Catalina Radiology
Tucson Arizona

Ben 08.24.23 Reply

Thanks for your thoughtful comment. I disagree with your assessment of Dr. Rao’s premise: game theory is a branch of mathematics that studies the behavior of “rational” agents. It analyses decision-making in the context of games, which can be a helpful proxy for understanding broader decision-making. It has nothing to say about morality, and mathematical explanations of “optimal” choices are not prescriptive or even idealized. The Nash equilibrium is what John Nash won the Nobel prize for; in many games, including the Prisoner’s Dilemma, it is often explicitly not a “good” thing.

If you read the posts on this site, I think you would see that I share your opinions on selling practices, taking jobs with certain nefarious corporate entities, and the race to the bottom that both hasten.

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